{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using device: cpu\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Training Progress:   0%|          | 0/20 [00:00<?, ?it/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Step: 15 | Loss: 0.129: 100%|██████████| 20/20 [00:36<00:00,  1.82s/it]\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from torch import autograd\n",
    "from torch.utils.tensorboard import SummaryWriter\n",
    "from tqdm import tqdm\n",
    "import matplotlib.pyplot as plt\n",
    "from kan import KAN, LBFGS\n",
    "\n",
    "device = torch.device(\"cpu\")\n",
    "print(\"Using device:\", device)\n",
    "\n",
    "rho = torch.tensor(1.0, device=device)\n",
    "nu = torch.tensor(0.01, device=device)\n",
    "eps = torch.tensor(1e-8, device=device)\n",
    "\n",
    "width, height = 10.0, 2.0\n",
    "num_points_x, num_points_y = 100, 20\n",
    "\n",
    "x = torch.linspace(0, width, num_points_x, device=device)\n",
    "y = torch.linspace(0, height, num_points_y, device=device)\n",
    "X, Y = torch.meshgrid(x, y, indexing='ij')\n",
    "coordinates = torch.stack([X.flatten(), Y.flatten()], dim=1)\n",
    "\n",
    "model = KAN(width=[2,3,3, 3], grid=5, k=10, grid_eps=1.0,\n",
    "            noise_scale_base=0.25).to(device)\n",
    "\n",
    "\n",
    "def batch_jacobian(func, x, create_graph=False):\n",
    "    # x in shape (Batch, Length)\n",
    "    def _func_sum(x):\n",
    "        return func(x).sum(dim=0)\n",
    "    return autograd.functional.jacobian(_func_sum, x, create_graph=create_graph).permute(1, 0, 2)\n",
    "\n",
    "\n",
    "def navier_stokes_residuals(coords):\n",
    "    y_pred = model(coords)\n",
    "    grads = batch_jacobian(model, coords)\n",
    "\n",
    "    u, v, p = y_pred[:, 0], y_pred[:, 1], y_pred[:, 2]\n",
    "    u_x, u_y = grads[:, 0, 0], grads[:, 0, 1]\n",
    "    v_x, v_y = grads[:, 1, 0], grads[:, 1, 1]\n",
    "    p_x, p_y = grads[:, 2, 0], grads[:, 2, 1]\n",
    "\n",
    "    continuity = u_x + v_y + eps * p # Assuming incompressibility (no source/sink terms)\n",
    "    x_momentum = u * u_x + v * u_y + (1 / rho) * p_x - nu * (u_x + u_y)\n",
    "    y_momentum = u * v_x + v * v_y + (1 / rho) * p_y - nu * (v_x + v_y)\n",
    "\n",
    "    #coords are a Nx2 tensor where each row is [x, y]\n",
    "    no_slip_mask = (coords[:, 1] == 0) | (coords[:, 1] == height)  # No-slip at top and bottom\n",
    "    inlet_mask = (coords[:, 0] == 0)  # Inlet at x = 0\n",
    "    outlet_mask = (coords[:, 0] == width)  # Outlet at x = width\n",
    "\n",
    "    # Applying boundary conditions\n",
    "    no_slip_loss = torch.mean(u[no_slip_mask] ** 2 + v[no_slip_mask] ** 2)  # u and v should be zero\n",
    "    inlet_loss = torch.mean((u[inlet_mask] - 1) ** 2)  # u should be 1, v should be 0 at inlet\n",
    "    outlet_pressure_loss = torch.mean(p[outlet_mask] ** 2)  # p should be 0 at outlet\n",
    "\n",
    "    # Combine all losses\n",
    "    bc_loss = no_slip_loss + inlet_loss + outlet_pressure_loss\n",
    "    total_loss = torch.mean(continuity ** 2 + x_momentum ** 2 + y_momentum ** 2) + bc_loss\n",
    "    return total_loss\n",
    "\n",
    "\n",
    "\n",
    "writer = SummaryWriter()\n",
    "\n",
    "\n",
    "def train():\n",
    "    optimizer = LBFGS(model.parameters(), lr=1,\n",
    "                      history_size=10, line_search_fn=\"strong_wolfe\", tolerance_grad=1e-32, tolerance_change=1e-32, tolerance_ys=1e-32)\n",
    "    steps = 20\n",
    "    pbar = tqdm(range(steps), desc='Training Progress')\n",
    "\n",
    "    for step in pbar:\n",
    "        def closure():\n",
    "            optimizer.zero_grad()\n",
    "            loss = navier_stokes_residuals(coordinates)\n",
    "            loss.backward()\n",
    "            return loss\n",
    "\n",
    "        optimizer.step(closure)\n",
    "        if step % 5 == 0:\n",
    "            current_loss = closure().item()\n",
    "            pbar.set_description(\"Step: %d | Loss: %.3f\" %\n",
    "                                 (step, current_loss))\n",
    "            writer.add_scalar('Loss/train', current_loss, step)\n",
    "\n",
    "\n",
    "train()\n",
    "\n",
    "writer.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_pred = model(coordinates)[:, 0].detach().reshape(\n",
    "    num_points_x, num_points_y).T\n",
    "\n",
    "v_pred = model(coordinates)[:, 1].detach().reshape(\n",
    "    num_points_x, num_points_y).T\n",
    "\n",
    "\n",
    "magnitude = torch.sqrt(u_pred ** 2 + v_pred ** 2)\n",
    "\n",
    "plt.figure(figsize=(10, 5))  # Set the figure size as needed\n",
    "plt.imshow(magnitude, extent=(0, width, 0, height), origin='lower', cmap='viridis')\n",
    "plt.colorbar()  # Add a colorbar to show the magnitude scale\n",
    "plt.title('Velocity Magnitude Contour')\n",
    "plt.xlabel('Width')\n",
    "plt.ylabel('Height')\n",
    "plt.axis('equal')  # Ensure the plot has equal scaling\n",
    "plt.tight_layout()  # Adjust layout to prevent overlap\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x600 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
